Simplify the radical expression.
√63x^15y^9/7xy^11
A. 8x^7 y^4 √xy / √7xy^11
B. 3x^7 / y
C. 9x^7 / y
D. 9x^7y
C. 9x^7 / y
Since they said "radical expression" I assume they meant
√(63x^15y^9/(7xy^11))
= √(9x^14/y^2)
= 3x^7/y
So, B
To simplify the radical expression √(63x^15y^9) / (7xy^11), we can start by splitting the numerator and denominator into separate square roots:
√(63x^15y^9) / (7xy^11) = (√(63) √(x^15) √(y^9)) / (√(7) √(x) √(y^11))
Next, we can simplify the square roots of each factor:
√63 = √(9*7) = √9 * √7 = 3√7
√x^15 = √(x^14 * x) = x^7 * √x
√y^9 = √(y^8 * y) = y^4 * √y
√7 = √7
√x = √x
√y^11 = √(y^10 * y) = y^5 * √y
Substituting these simplified square roots back into the original expression:
(3√7 x^7 y^4 √x √y) / (7xy^5 √x √y)
Now, we can cancel out common terms in the numerator and denominator:
(3√7 x^7 y^4 √x √y) / (7xy^5 √x √y) = (3√7 x^7 y^4) / (7xy^5)
Lastly, we can simplify the expression by canceling out the common terms:
(3√7 x^7 y^4) / (7xy^5) = 3x^7 y^4 / 7y^5 = 3/7 * x^7 / y
Therefore, the simplified radical expression is option B: 3x^7 / y.
To simplify the given radical expression, we can follow these steps:
Step 1: Simplify the numerator and the denominator separately.
√63 can be simplified as follows:
√(9 x 7) = √9 x √7 = 3√7
x^15 can be rewritten using the rule of exponents:
x^15 = x^(3 x 5) = (x^3)^5 = x^3 x x^3 x x^3 x x^3 x x^3 = x^3 x x^3 x x^3 x x^3 x x^3
y^9 can be rewritten similarly:
y^9 = y^(3 x 3) = (y^3)^3 = y^3 x y^3 x y^3
Step 2: Simplify the expression further by canceling common factors between the numerator and the denominator.
Canceling common factors:
(3√7x^3y^3) / (7xy^11)
Step 3: Simplify the expression by removing any duplicate variables.
Removing duplicate variables:
(3√7x^3y^3) / (7xy^11) = (3√7x^(3-1)y^(3-11)) / 7 = (3√7x^2 / 7y^8)
So, simplifying the given radical expression, we get:
√63x^15y^9 / 7xy^11 = (3√7x^2 / 7y^8)
Therefore, the correct answer is:
A. 8x^7 y^4 √xy / √7xy^11